Francisco Antonio Bezerra Coutinho

Modelling the control strategies against dengue in Singapore

Notified cases of dengue infections in Singapore reached historical highs in 2004 (9459 cases) and 2005 (13,817 cases) and the reason for such an increase is still to be established. We apply a mathematical model for dengue infection that takes into account the seasonal variation in incidence, characteristic of dengue fever, and which mimics the 2004-2005 epidemics in Singapore. We simulated a set of possible control strategies and confirmed the intuitive belief that killing adult mosquitoes is the most effective strategy to control an ongoing epidemic. On the other hand, the control of immature forms was very efficient in preventing the resurgence of dengue epidemics. Since the control of immature forms allows the reduction of adulticide, it seems that the best strategy is to combine both adulticide and larvicide control measures during an outbreak, followed by the maintenance of larvicide methods after the epidemic has subsided. In addition, the model showed that the mixed strategy of adulticide and larvicide methods introduced by the government seems to be very effective in reducing the number of cases in the first weeks after the start of control.

The risk of yellow fever in a dengue-infested area

Yellow fever and dengue are viral infections that in urban centres are transmitted by the same arthropod vector, a mosquito of the genus Aedes. In order to estimate the risk of an epidemic of urban yellow fever in a dengue-infested area we calculated the threshold in the basic reproduction number, R0, of dengue, above which any single sylvatic yellow fever-infected individual will trigger an urban yellow fever epidemic. Specifically, we analysed the relationship between the extrinsic incubation period and the duration of viraemia, from which it is possible to define the R0 for dengue that would also suggest an outbreak potential for yellow fever. We also calculated the critical proportion of people to vaccinate against yellow fever in order to prevent an epidemic in a dengue-endemic area. The theory proposed is illustrated by the case of São Paulo State in southern Brazil, where dengue is endemic and the risk of urban yellow fever is already imminent.

Dengue and the risk of urban yellow fever reintroduction in São Paulo State, Brazil

OBJECTIVE To propose a mathematical method for the estimation of the Basic Reproduction Number, R0, of urban yellow fever in a dengue-infested area. METHODS The method is based on the assumption that, as the same vector (Aedes aegypti) causes both infections, all the quantities related to the mosquito, estimated from the initial phase of dengue epidemic, could be applied to yellow fever dynamics. It is demonstrated that R0 for yellow fever is, on average, 43% lower than that for dengue. This difference is due to the longer dengue viremia and its shorter extrinsic incubation period. RESULTS In this study the analysis was expanded to the epidemiological situation of dengue in S o Paulo in the year 2001. The total number of dengue cases increased from 3,582 in 2000 to 51,348 in 2001. It was then calculated R0 for yellow fever for every city which have shown R0 of dengue greater than 1. It was also estimated the total number of unprotected people living in highly risky areas for urban yellow fever. CONCLUSIONS Currently there is a great number of non-vaccinated people living in Aedes aegypti infested area in the state of São Paulo.

The Risk of Chikungunya Fever in a Dengue‐Endemic Area

BACKGROUND Chikungunya, an alphavirus of the Togaviridae family, causes a febrile disease transmitted to humans by the bite of infected Aedes mosquitoes. This infection is reaching endemic levels in many Southeast Asian countries. Symptoms include sudden onset of fever, chills, headache, nausea, vomiting, joint pain with or without swelling, low back pain, and rash. According to the World Health Organization, there are 2 billion people living in Aedes-infested areas. In addition, traveling to these areas is popular, making the potential risk of infections transmitted by the bite of infected Aedes mosquitoes very high. METHODS We proposed a mathematical model to estimate the risk of acquiring chikungunya fever in an Aedes-infested area by taking the prevalence of dengue fever into account. The basic reproduction number for chikungunya fever R(0chik) can be written as a function of the basic reproduction number of dengue R(0dengue) by calculating the ratio R(0chik)/R(0dengue). From R(0chik), we estimated the force of infection and the risk of acquiring the disease both for local residents of a dengue-endemic area and for travelers to this area. RESULTS We calculated that R(0chik) is 64.4% that of R(0dengue). The model was applied to a hypothetical situation, namely, estimating the individual risk of acquiring chikungunya fever in a dengue-endemic area, both for local inhabitants (22% in steady state) and for visiting travelers (from 0.31% to 1.23% depending on the time spent in the area). CONCLUSIONS The method proposed based on the output of a dynamical model is innovative and provided an estimation of the risk of infection, both for local inhabitants and for visiting travelers.

Modelling the Dynamics of Leishmaniasis Considering Human, Animal Host and Vector Populations

Some of the vector-borne infections with public health importance involve an animal reservoir. This work describes, through a compartimental model, the dynamics of leishmaniasis considering the interactions between the three populations involved, namely the sandfly, the domestic dog (as the principal intermediate host), and the human population. An expression for the Basic Reproduction Ratio (R0), which takes into account the time delay representing the extrinsic incubation period of the parasite in the vector, is presented. Numerical simulation, equilibrium and stability analysis provided insights into the transmission dynamics of the infection that can help in the design of control strategies.

Threshold conditions for infection persistence in complex host-vectors interactions.

As classically defined by Macdonald in the early 1950s, for the case of diseases with one vector and one host, the Basic Reproduction Number, R0, is defined as the number of secondary infections caused by a single infective of the same type (vector or host) during its infectiousness period in an entirely susceptible population. In the case of a disease which has one vector and one host, it is easy to show that R0 coincides with the threshold for the establishment of an endemic state: if R0 > 1 (< 1), the disease can invade (cannot invade) the host population. In this paper we examine various epidemic situations in which there are more than one vector and/or host. We show that in those more complex systems it is not possible to deduce a single R0 but rather a threshold for infection persistence which is a composite of several quantities closely related to the classical expression of R0. Another definition of R0 given by Diekmann, Heesterbeek and Metz, and denoted in this paper R0NGO is discussed and applied as an alternative to calculate the thresholds for infection establishment.

Generalized point interactions in one-dimensional quantum mechanics

There is a four-parameter family of point interactions in one-dimensional quantum mechanics. They represent all possible self-adjoint extensions of the kinetic energy operator. If time-reversal invariance is imposed, the number of parameters is reduced to three. One of these point interactions is the familiar function potential but the other generalized ones do not seem to be widely known. We present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so-called interaction. We emphasize that there is little resemblance between the interaction and what its name suggests.

The basic reproduction ratio of HIV among intravenous drug users

A new approach for the estimation of the Basic Reproduction Ratio R0 for HIV among intravenous drug users (IVDU) is proposed. This approach is based in an adaptation of the models proposed by Ross and Macdonald for vector-borne infections. A straightforward adaptation of Macdonalds model is presented first: biological vectors are replaced by needles and syringes and we consider a homogeneous population of IVDUs; next we present a modified model where several heterogeneities are considered. Some of those heterogeneities are due to intrinsic differences between needles and syringes and biological vectors; others, such as those related to movements of individuals between communities, should apply to both biological vectors and injection apparatuses. An example of the calculations of R0 for a real IVDUs community is presented.

Dynamics of the 2006/2007 dengue outbreak in Brazil

We analyzed dengue incidence in the period between October 2006-July 2007 of 146 cities around the country were Larval Index Rapid Assay (LIRA) surveillance was carried out in October 2006. Of these, we chosen 61 cities that had 500 or more cases reported during this period. We calculated the incidence coefficient, the force of infection (lambda) and the basic reproduction number (R0) of dengue in those 61 cities and correlated those variables with the LIRA. We concluded that lambda and R0 are more associated with the number of cases than LIRA. In addition, the average R0 for the 2006/2007 dengue season was almost as high as that calculated for the 2001/2002 season, the worst in Brazilian history.

Modeling the impact of global warming on vector-borne infections

Global warming will certainly affect the abundance and distribution of disease vectors. The effect of global warming, however, depends on the complex interaction between the human host population and the causative infectious agent. In this work we review some mathematical models that were proposed to study the impact of the increase in ambient temperature on the spread and gravity of some insect-transmitted diseases.